Easy with DrawGraphics from my web site below.
Needs["DrawGraphics`DrawingMaster`"]
First we draw the 3D surface with z==0 and convert the Polygons to 2D
polygons.
surface =
ParametricDraw3D[{u - v^2, u v, 0}, {u, -1, 1}, {v, -1,
1}] /. {x_?NumberQ, y_?NumberQ, _?NumberQ} -> {x, y};
Then we draw the resulting surface in 2D. Mathematica outlines Polygons in
3D but does not outline them in 2D. The DrawGraphics routine PolygonOutline
will add the edges. I used LightGray so the edges would be subdued.
Draw2D[
{LightBlue, surface,
surface // PolygonOutline[LightGray]},
Frame -> True,
PlotLabel -> "Parametric 2D Area",
Background -> Linen,
ImageSize -> 350];
David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/
From: Narasimham G.L. [mailto:mathma18 at hotmail.com]
To: mathgroup at smc.vnet.net
Is it possible to plot like :) ParametricPlot2D {x,y}=f(u,v), where
u,v are two parameters? At present, I am plotting by setting z=0 in a
3D plot e.g.,
ParametricPlot3D[{u-v^2,u v,0},{u,-1,1},{v,-1,1},ViewPoint->{0,0,4}] ;
But it adds colour to the domain that would have become a surface in
3D had z been non-zero. Actually I like to see clean plots, no matter
if there are self-intersections.What is the simplest plot command
recommended in such cases?